The random walk on the boundary Monte Carlo method has been successfully used for solving boundary-value problems. This method has significant advantages when compared to random walks on spheres, balls or a grid, when solving exterior problems, or when solving a problem at an arbitrary number of points using a single random walk. In this paper we study the properties of the method when we use quasirandom sequences instead of pseudorandom numbers to construct the walks on the boundary. Theoretical estimates of the convergence rate are given and numerical experiments are presented in an attempt to confirm the convergence results. The numerical results show that for "walk on the boundary" quasirandom sequences provide a slight improvement over ordinary Monte Carlo.
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